My work

Currently, I study coherent dipolar energy transfer between resonant levels of ultra-cold Rydberg atoms (Scholak, Wellens, and Buchleitner 2014), specifically, of the non-radiative exchange of an excitation among a large number of randomly distributed atoms. I conduct large-scale numerical surveys on the statistics of clouds with a large number of atoms $N$ and compare them to results of established random matrix theories, Euclidean and stable random matrix theory, for instance. I also work on analytical treatments for the asymptotic limit, where $N \to \infty$.

During my PhD, I worked on excitonic energy transport in disordered networks (Scholak et al. 2011; Scholak 2011), in particular, pigment-protein complexes with strong dipole-dipole interactions. I employed evolution strategies to numerically optimize the energy transport in these systems. I got heavily involved in the ongoing debate on the mechanisms that drive efficient transport across photosynthetic complexes.

In the group of Paul Brumer, one of my main concerns has been the substantiation of quantum coherence effects in the control of atomic and molecular processes with lasers, i.e. quantum coherent control (Scholak and Brumer 2014). To this end, I integrated coherent control ideas with concepts of quantum interferometry, in particular, the complementarity of waves and particles, suggesting the possibility to observe non-trivial quantum effects in new scenarios of two-color phase control.

Publications

In preparation

Addressed the long standing issue of the significance of quantum coherence and nonclassical effects in scenarios of coherent phase control ⋅ Showed that two-color weak-field phase control, the archetype of the all-optical control methods, is an analogue of a purely classical control phenomenon ⋅ Introduced a new, unifying framework called the coherent control interferometer ⋅ Studied quantitative wave-particle complementarity in the setting of coherent phase control ⋅ Designed two new quantum coherent control scenarios: quantum erasure and quantum delayed choice coherent control ⋅ Showed that the nonclassicality and the genuine randomness of these new scenarios can be certified by Bell inequality tests.

@unpublished{scholak2015nonclassical,
annote = {Addressed the long standing issue of the significance of quantum coherence and nonclassical effects in scenarios of coherent phase control ⋅ Showed that two-color weak-field phase control, the archetype of the all-optical control methods, is an analogue of a purely classical control phenomenon ⋅ Introduced a new, unifying framework called the coherent control interferometer ⋅ Studied quantitative wave-particle complementarity in the setting of coherent phase control ⋅ Designed two new quantum coherent control scenarios: quantum erasure and quantum delayed choice coherent control ⋅ Showed that the nonclassicality and the genuine randomness of these new scenarios can be certified by Bell inequality tests.},
author = {Scholak, Torsten and Brumer, Paul},
date-added = {2015-03-01 17:01:29 +0000},
date-modified = {2015-03-01 17:02:42 +0000},
month = jan,
note = {in preparation},
title = {Nonclassical interference versus classical nonlinear response: When is coherent control truly quantum?},
year = {2015}
}

Found that the nature of excitation energy transfer (EET) in a Rydberg gas can be controlled via the dipole blockade effect ⋅ Analyzed the ensemble-averaged mean-square displacement ⋅ Studied the spatial distribution of the system’s eigenstates.

Studied spectral structure underlying excitonic energy transfer in ultracold Rydberg gases ⋅ Found evidence for a critical energy that separates delocalized eigenstates from states that are localized at pairs or clusters of atoms separated by less than the typical nearest-neighbor distance ⋅ Discovered that the dipole blockade effect in Rydberg gases can be leveraged to manipulate the localization transition.

The spectral structure underlying excitonic energy transfer in ultracold Rydberg gases is studied numerically, in the framework of random matrix theory, and via self-consistent diagrammatic techniques. Rydberg gases are made up of randomly distributed, highly polarizable atoms that interact via strong dipolar forces. Dynamics in such a system is fundamentally different from cases in which the interactions are of short range, and is ultimately determined by the spectral and eigenvector structure. In the energy levels’ spacing statistics, we find evidence for a critical energy that separates delocalized eigenstates from states that are localized at pairs or clusters of atoms separated by less than the typical nearest-neighbor distance. We argue that the dipole blockade effect in Rydberg gases can be leveraged to manipulate this transition across a wide range: As the blockade radius increases, the relative weight of localized states is reduced. At the same time, the spectral statistics, in particular, the density of states and the nearest-neighbor level-spacing statistics, exhibits a transition from approximately a 1-stable Lévy to a Gaussian orthogonal ensemble. Deviations from random matrix statistics are shown to stem from correlations between interatomic interaction strengths that lead to an asymmetry of the spectral density and profoundly affect localization properties. We discuss approximations to the self-consistent Matsubara-Toyozawa locator expansion that incorporate these effects.

We consider the role of quantum mechanics in a specific coherent control scenario, designing a “coherent control interferometer” as the essential tool that links coherent control to quantum fundamentals. Building upon this allows us to rigorously display the genuinely quantum nature of a generalized weak-field coherent control scenario (utilizing 1 vs. 2 photon excitation) via a Bell-CHSH test. Specifically, we propose an implementation of “quantum delayed-choice” in a bichromatic alkali atom photoionization experiment. The experimenter can choose between two complementary situations, which are characterized by a random photoelectron spin polarization with particle-like behavior on the one hand, and by spin controllability and wave-like nature on the other. Because these two choices are conditioned coherently on states of the driving fields, it becomes physically unknowable, prior to measurement, whether there is control over the spin or not.

Through simulations of quantum coherent transport on disordered molecular networks, we show that three dimensional structures characterized by centro-symmetric Hamiltonians exhibit on average higher transport efficiencies than random configurations. Furthermore, configurations that optimize constructive quantum interference from input to output site yield systematically shorter transfer times than classical transport induced by ambient dephasing noise.

Discussed the role of disorder for the optimization of exciton transport in the FMO (Fenna-Matthews-Olson) light harvesting complex ⋅ Demonstrated the existence of a small fraction of optimal, though highly asymmetric, non-periodic conformations, which yield near-to-optimal coherent excitation transport.

We discuss the possibly constructive role of disorder for the optimization of exciton transport in the FMO (Fenna􏰂Matthews􏰂Olson) light harvesting complex. Our analysis, which models the FMO as a 3D random graph, demonstrates the existence of a small fraction of optimal, though highly asymmetric, non-periodic conformations, which yield near-to-optimal coherent excitation transport. We argue that, on transient time scales, such quantum interference enhanced transport does always better than stochastic activation.

Investigated coherent and incoherent excitation transfer in a random network with dipole-dipole interactions as a model system describing energy transport, e.g., in photosynthetic light-harvesting complexes or gases of cold Rydberg atoms.

We investigate coherent and incoherent excitation transfer in a random network with dipole–dipole interactions as a model system describing energy transport, e.g., in photosynthetic light-harvesting complexes or gases of cold Rydberg atoms. For this purpose, we introduce and compare two different measures (the maximum output probability and the average transfer time) for the efficiency of transport from the input to the output site. We especially focus on optimal configurations which maximize the transfer efficiency and the impact of dephasing noise on the transport dynamics. For most configurations of the random network, the transfer efficiency increases when adding noise, giving rise to essentially classical transport. These noise-assisted configurations are, however, systematically less efficient than the optimal configurations. The latter reach their highest efficiency for purely coherent dynamics, i.e. in the absence of noise.

Showed that configurations of a random molecular network that optimize constructive quantum interference from input to output site yield systematically shorter transfer times than classical transport induced by ambient dephasing noise.

Stunningly large exciton transfer rates in the light harvesting complex of photosynthesis, together with recent experimental 2D spectroscopic data, have spurred a vivid debate on the possible quantum origin of such efficiency. Here we show that configurations of a random molecular network that optimize constructive quantum interference from input to output site yield systematically shorter transfer times than classical transport induced by ambient dephasing noise.

Showed that finite-size, disordered molecular networks can mediate highly efficient, coherent excitation transfer that is robust against ambient dephasing and is associated with strong multisite entanglement ⋅ Offered an explanation for the efficient energy transfer in the photosynthetic Fenna-Matthews-Olson complex.

We show that finite-size, disordered molecular networks can mediate highly efficient, coherent excitation transfer which is robust against ambient dephasing and associated with strong multisite entanglement. Such optimal, random molecular conformations may explain efficient energy transfer in the photosynthetic Fenna-Matthews-Olson complex.

Described a general method of realizing entanglement witnesses in terms of the interference pattern of a single quantum probe.

We describe a general method of realizing entanglement witnesses in terms of the interference pattern of a single quantum probe. After outlining the principle, we discuss specific realizations both with electrons in mesoscopic Aharonov-Bohm rings and with photons in standard Young’s double-slit or coherent-backscattering interferometers.

Showed that excitation transport across molecular networks mimicking the FMO light-harvesting complex can be enhanced by quantum coherence on transient timescales.

This chapter reviews the essential ingredients of quantum transport in disordered systems, and introduces measures of quantum coherence and entanglement in multisite systems. It explains excitation transport in Fenna–Matthews–Olsen (FMO)-like structures under strictly coherent conditions as well as in presence of a dephasing environment. The statistical treatment of excitation transport across a molecular network mimicking the FMO light-harvesting complex shows the potential of quantum coherence to enhance transport, on transient timescales. The transfer probability thus achieved can reach 100%—a value unachievable by classically diffusive, unbiased transport. Furthermore, because such quantum transfer is brought about by constructive multipath interference along intermediate sites of the molecular complex, coherent quantum transport is certainly faster than classically diffusive transport for comparable inter-site coupling strengths. Taking both transfer probability and transfer time together, coherence thus defines levels of quantum efficiency unreached by a classical transport process on the same network. The quantum coherence holds the potential to steer quantum transport efficiencies in engineered devices as abundant in semiconductor technology.

A current and actively discussed issue are the mechanisms that drive efficient transport across photosynthetic light-harvesting complexes. Recent experiments detected long-lived quantum coherence in these systems, in the process rendering some long-accepted textbook knowledge obsolete: Although the very fabric of life—atoms and molecules—is of a quantum nature, these effects were thought to be irrelevant for most biological processes, simply because they operate at room temperature and involve vastly many degrees of freedom. Could nature, in order to enhance the efficiency of principal tasks, take advantage of quantum mechanical coherent dynamics?
In this thesis, we will investigate the transport properties of an ensemble of spatially disordered, finitely sized molecular networks with dipolar interactions in order to model energy transport in photosynthetic complexes in consideration of the variability of organic samples and the experimental uncertainties. For this task, we employ and compare several measures of transport efficiency. In contrast to the widely used hypothesis stating that quantum coherence effects generally lead to localization and thus hinder transport, we will identify certain rare optimal conformations featuring fast and perfectly efficient transport of energy—solely by means of constructive quantum interference. Furthermore, we will unveil that efficient transport is always associated with the build-up of strong multisite entanglement. Adding dephasing noise—which gradually destroys interference and thereby gives rise to essentially classical transport—increases the transport efficiency of most configurations, but, as we show, the highest efficiencies are attained only by the optimal configurations in case of purely coherent dynamics, i.e., in the absence of noise. Finally, we attempt to extrapolate the transport statistics to infinitely sized systems.

Talks and posters

Rydberg atoms are highly excited neutral atoms with exceptional properties. Not long ago, interest in Rydberg atoms was limited to their spectroscopic properties. However, in recent years, Rydberg science has become increasingly interdisciplinary. It is now a rapidly progressing research area at the crossroads of atomic, optical, condensed matter physics, and quantum information science with a host of possible applications. Groundbreaking experiments demonstrate the promise of Rydberg systems not only for quantum information processing, but also for exploring the long-range nature of the strong Rydberg-Rydberg interaction that gives rise to many-particle correlations and excitation energy transfer (EET).
After an introduction to Rydberg physics, I will focus on our theoretical research work on the quantum-coherent EET through "frozen" Rydberg gas clouds, in which the atoms have been slowed down almost to a full stop. For these systems, I reveal how the nature of EET can be controlled via the dipole blockade. This effect is known to lead to a proximity-dependent suppression of Rydberg excitations and the emergence of ordered excitation structures from a disordered gas. For weak blockade, we predict the transient localization of EET on small clusters of two or more atoms. For stronger blockade, however, EET will be significantly faster, since the excitations are efficiently migrated by delocalized states. I will illustrate this with our results on the spectral and eigenvector structure of the Rydberg gas ensemble. My talk is concluded by an outline of upcoming milestones and their challenges.

The spectral signatures of excitonic energy transfer in ultra-cold Rydberg gas clouds are studied numerically, in the framework of random matrix theory, and via self-consistent diagrammatic techniques. Rydberg gases are made up of randomly distributed, highly polarizable atoms that interact via strong long-range dipolar forces. Dynamics in such a system is fundamentally different from cases in which the interactions are short-range. In the spectral level spacing statistics, we find evidence for a critical energy that separates delocalized eigenstates from states that are localized at pairs or clusters of atoms separated by less than the typical nearest-neighbor distance. We argue that the dipole blockade effect in Rydberg gases can be leveraged to manipulate this transition across a wide range: As the blockade radius increases, the degree of localization in the system is reduced. At the same time, the spectral statistics – in particular, the density of states and the nearest neighbor level spacing statistics – change their approximate agreement from the 1-stable Lévy to the Gaussian orthogonal random matrix ensemble. Deviations to random matrix statistics are identified to stem from corre- lations between atomic interactions that lead to an asymmetry of the spectral density and are also shown to have a profound influence on localization. We solve approximations to the self-consistent Matsubara-Toyozawa locator expansion that incorporate these effects.

The spectral signatures of excitonic energy transfer in ultra-cold Rydberg gas clouds are studied numerically, in the framework of random matrix theory, and via self-consistent diagrammatic techniques. Rydberg gases are made up of randomly distributed, highly polarizable atoms that interact via strong long-range dipolar forces. Dynamics in such a system is fundamentally different from cases in which the interactions are short-range. In the spectral level spacing statistics, we find evidence for a critical energy that separates delocalized eigenstates from states that are localized at pairs or clusters of atoms separated by less than the typical nearest-neighbor distance. We argue that the dipole blockade effect in Rydberg gases can be leveraged to manipulate this transition across a wide range: As the blockade radius increases, the degree of localization in the system is reduced. At the same time, the spectral statistics – in particular, the density of states and the nearest neighbor level spacing statistics – change their approximate agreement from the 1-stable Lévy to the Gaussian orthogonal random matrix ensemble. Deviations to random matrix statistics are identified to stem from corre- lations between atomic interactions that lead to an asymmetry of the spectral density and are also shown to have a profound influence on localization. We solve approximations to the self-consistent Matsubara-Toyozawa locator expansion that incorporate these effects.

What is the role of quantum coherence for the mechanisms underlying efficient energy transport though photosynthetic light-harvesting complexes? To explore this question, we conduct a large-scale statistical survey of excitation transport in ensembles of spatially disordered, finitely sized molecular networks with dipolar interactions in the presence of tunable dephasing noise, and we compare the efficiency of noise-assisted transport with that achievable by means of constructive quantum interference. In contrast to the common presumption that coherent effects generally lead to localization and thus to suppression of transport, we prove the existence of certain rare optimal molecular configurations that mediate highly efficient coherent excitation transport. Although dephasing noise – which gradually destroys interference and thereby gives rise to essentially classical transport – enhances the efficiency of most configurations in our statistical ensemble, the detected optimal configurations yield systematically higher transport efficiencies and attain the maximum efficiency in the absence of noise. These insights – combined with recent experimental demonstrations of long-lived coherence in certain light-harvesting structures – provide a strong hint that nature takes advantage of quantum mechanical coherent dynamics in order to enhance the efficiency of principal tasks.

Our study of coherent excitation transfer in finitely sized disordered molecular networks reveals certain optimal conformations that feature fast and perfectly efficient transport of energy – solely by means of constructive quantum interference. The properties and mechanics of these remarkable conformations are the subject of this talk. Our insights may help to better understand the efficient energy transfer in photosynthetic light-harvesting complexes.

———, 2010, “Entanglement-Enhanced Energy Transport” (talk given at the conference on “New Perspectives In Quantum Statistics And Correlations” at the Akademie der Wissenschaften in Heidelberg, Germany).

In many areas of physics we witness dramatic differences between classical and quantum transport. In general, we expect quantum features to fade away on large scales, due to the ever more unavoidable – and detrimental – influence of the environment which scrambles relative phases and damps quantum amplitudes. Recent experimental evidence suggests, however, that the functional efficiency of large biomolecular units may stem from quantum coherence phenomena, despite strong environment coupling. We explain such efficiency, under the assumption that evolution is able to steer finite size three dimensional systems into molecular conformations with optimal coherent transport properties. It turns out that such optimal conformations are characterized by specific, optimal entanglement properties between different sites of the molecular complex.

In many areas of physics we witness dramatic differences between classical and quantum transport. In general, we expect quantum features to fade away on large scales, due to the ever more unavoidable – and detrimental – influence of the environment which scrambles relative phases and damps quantum amplitudes. Recent experimental evidence suggests, however, that the functional efficiency of large biomolecular units may stem from quantum coherence phenomena, despite strong environment coupling. We explain such efficiency, under the assumption that evolution is able to steer finite size three dimensional systems into molecular conformations with optimal coherent transport properties. It turns out that such optimal conformations are characterized by specific, optimal entanglement properties between different sites of the molecular complex.

We study coherent dipolar energy transfer between resonant levels of Rydberg atoms. We determine the transport properties by examining the spectral structure and the associated eigenfunctions. To highlight the impact of disorder on the Rydberg exciton transport, we introduce a disorder parameter allowing us to switch continuously from an ordered to a completely disordered sample of atoms. Special attention is dedicated to the transition from diffusive to non-diffusive transport, as well as to the metamorphosis of the nearest-neighbor level spacing distribution from Wigner to Poisson.

We study coherent dipolar energy transfer between resonant levels of Rydberg atoms. We determine the transport properties by examining the spectral structure and the associated eigenfunctions. To highlight the impact of disorder on the Rydberg exciton transport, we introduce a disorder parameter allowing us to switch continuously from an ordered to a completely disordered sample of atoms. Special attention is dedicated to the transition from diffusive to non-diffusive transport, as well as to the metamorphosis of the nearest-neighbor level spacing distribution from Wigner to Poisson.

We study the light-scattering dynamics of two tightly trapped atoms with internal spin degrees of freedom. The aim is to manipulate populations and coherences by a selective tuning of photon field parameters like polarization. We are particularly interested in the preparation of entanglement and its subsequent witnessing by interaction with the driving laser field.

We propose to realize entanglement witnesses in terms of the interference pattern of a single quantum probe. After giving a conceptional recipe, we discuss possible realizations both with electrons in mesoscopic Aharonov-Bohm rings and with photons in standard Young’s double-slit or coherent-backscattering interferometers.

We study the scattering of a single photon by two atoms whose spin-1/2 ground states are an entangled qubit pair. A lower bound on its concurrence can be obtained by measuring the visibility of the coherent-backscattering interference fringes in a suitable polarization configuration.

We study the scattering of a single photon by two atoms whose spin-1/2 ground states are an entangled qubit pair. A lower bound on its concurrence can be obtained by measuring the visibility of the coherent-backscattering interference fringes in a suitable polarization configuration.